Ray Alder of Fates Warning did a side band called "Engine" and they recorded a hard rock version of The Cure's "Fascination Street". Peter Parada (whom I went to school with and is now with The Offsping) played drums:

but gosh, there are so many, I could be here all day:
Dream Theater's version of Ozzy's "Diary of a Madman"
Type O Negative's version of Neil Young's "Cinnamon Girl"
Judas Priest's version of the Joan Baez song "Diamonds and Rust".

But here is an odd one:
Rasputina did a version of Led Zepplin's "Rock and Roll" on just two cellos, voice and drums. It's really weird, and almost wrong, which is probably why they did it.
Here is a badly recorded live version: http://www.youtube.com/watch?v=OBbm1...eature=related

In another conversation there was mention of The Beatles's Tomorrow Never Knows and it reminded me of 801's outstanding cover of the song - Phil Manzanera, Simon Phillips, Eno, Francis Monkman - what a lineup!

nhzoso, I remember that Faith No More cover. Great stuff - hilarious clip too :)

Rascul, I saw your links, which lead me to his cover of Paranoid Android - the first few mins of it are incredible.

Paul, that Dread Zeppelin mashup is really something - and somehow you managed to tie in Led Zep covers with the John Cage cover :)